Simplify the expression.
4k2(–3k2 – 4k + 5)
A. –12k4 – 16k3 + 20k2
B. 12k4 – 16k3 + 9k2
C. –12k3 + 20k
D. k4 + 9k2
Powers are written this way:
12x^3
so I will assume you have 4k^2(–3k^2 – 4k + 5)
= -12k^4 - 16k^3 + 20k^2
Study the rules of powers, that is, what happens to the exponents
when I multiply two powers with the same base ?
You cannot simplify this expression because it is already simplified.
You can only expand this expression.
4 k² ( - 3 k² - 4 k + 5 ) = 4 k² ∙ ( - 3 k² ) + 4 k² ∙ ( - 4 k ) + 4 k² ∙ 5 =
4 ∙ ( - 3 ) ∙ k² ⁺ ² + 4 ∙ ( - 4 ) ∙ k² ⁺ ¹ + 20 k² = - 12 k⁴ - 16 k³ + 20 k²
To simplify the given expression 4k^2(-3k^2 - 4k + 5), we need to distribute the 4k^2 to each term inside the parentheses and then combine like terms. Here's how to do it step by step:
1. Distribute 4k^2 to each term inside the parentheses:
(4k^2) * (-3k^2) = -12k^4
(4k^2) * (-4k) = -16k^3
(4k^2) * (5) = 20k^2
2. Combine the terms after distributing:
-12k^4 - 16k^3 + 20k^2
Hence, the simplified expression is -12k^4 - 16k^3 + 20k^2, which corresponds to option A.